Question

polygon abcd reflects about line mn to make polygon efgh. what is the length of \\(\overline{fg}\\)?
a. 3 units
b. 3.2 units
c. 2.2 units
d. 2 units

Explanation:

Step1: Recall Reflection Property

Reflection is a rigid transformation, so corresponding sides of the original polygon and its image are congruent.

Step2: Identify Corresponding Sides

In polygon \(ABCD\) and its reflection \(EFGH\), side \(BC\) in \(ABCD\) corresponds to side \(FG\) in \(EFGH\).

Step3: Determine Length of \(BC\)

From the diagram, the length of \(BC\) is 2 units. So, \(FG = BC = 2\) units? Wait, no, wait. Wait, looking at the diagram again, \(BC\) is labeled as 2? Wait, no, maybe I misidentified. Wait, the original polygon \(ABCD\): \(AB = 3\), \(BC = 2\), \(CD = 2.2\), \(DA = 3.2\). When reflecting over line \(MN\) to get \(EFGH\), the corresponding side to \(BC\) is \(FG\)? Wait, no, maybe \(AB\) corresponds to \(EF\), \(BC\) to \(FG\), \(CD\) to \(GH\), \(DA\) to \(HE\). Wait, \(BC\) has length 2? Wait, the options: D is 2 units. Wait, but let me check again. Wait, the problem is about reflecting polygon \(ABCD\) over line \(MN\) to make \(EFGH\). So, reflection preserves length, so corresponding sides are equal. So, which side in \(ABCD\) corresponds to \(FG\) in \(EFGH\)? Looking at the positions, \(B\) reflects to \(F\), \(C\) reflects to \(G\), so \(BC\) reflects to \(FG\). So, length of \(BC\) is 2 units (from the diagram: \(BC\) is labeled with 2). Therefore, \(FG = BC = 2\) units? Wait, but the options: D is 2 units. Wait, but maybe I made a mistake. Wait, no, let's confirm. Reflection is a rigid transformation, so all corresponding sides are congruent. So, if \(BC\) is 2, then \(FG\) is 2. So the answer should be D? Wait, but let me check the diagram again. The original polygon \(ABCD\): \(AB = 3\), \(BC = 2\), \(CD = 2.2\), \(DA = 3.2\). So when reflected, \(FG\) corresponds to \(BC\), so \(FG = BC = 2\) units. So the length of \(FG\) is 2 units, which is option D.

Wait, but earlier I thought maybe I misread, but now confirming: reflection preserves side lengths, so corresponding sides are equal. \(BC\) is 2, so \(FG\) is 2.

Answer:

D. 2 units